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Abstract

Accepting the importance of Jim Greeno’s work, not just in this volume but throughout his career, I offer this commentary from the position of a researcher who first worked “from the inside out” and who now works “from the outside in.” My identity is that of a mathematics educator with a theoretical commitment to design research. To clarify, for almost seven years I collaborated with Paul Cobb, Koeno Gravemeijer and others in the execution of classroom design experiments in which I acted as the teacher. In these settings, I was working from the inside out to first, in action, make sense of students’ understandings so that I could planfully orchestrate classroom discussions. Later, I would conduct retrospective analyses of my interactions by analyzing from the “outside” what I had previously participated in on the “inside.” In these instances, I worked to understand both the students’ and my learning through normative patterns of engagement. The theoretical lens that I adopted for most of my analyses of the classroom is that of a social constructivist with a strong emphasis on tools. I find Greeno’s levels of accounts of cognition in interaction strengthen my previous orientation by more clearly articulating levels of a progression of conceptual understanding. However, I am left wondering what the means of support are for shifts between the levels. Clearly, having a way to analyze the students’ current abilities or ways of reasoning is crucial. However, I view it as necessary but insufficient for supporting learning. It is this stance that I take in my commentary.

Keywords

Teacher Learning Discourse Topic Proactive Role Heat Exhaustion Conceptual Growth 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgements

I would like to thank the teachers in the Madison School District who participate in the Vanderbilt Teacher Collaborative at Madison [http://www.vtcm.org]. The analysis reported in this paper was supported by the National Science Foundation under grant REC-0135062.

References

  1. Ball, D. (1993). With an eye on the mathematical horizon: Dilemmas of teaching elementary school mathematics. The Elementary School Journal, 93, 373–397.CrossRefGoogle Scholar
  2. Ball, D., & Cohen, D. (1999). Developing practice, developing practitioners: Towards a practice-based theory of professional education. In G. Sykes & L. Darling-Hammond (Eds.), Teaching as the learning profession: Handbook of policy and practice (pp. 3–32). San Francisco: Jossey-Bass.Google Scholar
  3. Brown, A. L. (1992). Design experiments: Theoretical and methodological challenges in creating complex interventions in classroom settings. Journal of the Learning Sciences, 2, 141–178.CrossRefGoogle Scholar
  4. Cobb, P., Confrey, J., diSessa, A., Lehrer, R., & Schauble, L. (2003). Design experiments in educational research. Educational Researcher, 32(1), 9–13.CrossRefGoogle Scholar
  5. Cobb, P., & McClain, K. (2001). An approach for supporting teachers’ learning in social context. In F. -L. Lin & T. Cooney (Eds.), Making sense of mathematics teacher education (pp. 207–232). Dordrecht: Kluwer Academic.Google Scholar
  6. Cobb, P., & Yackel, E. (1996). Constructivist, emergent, and sociocultural perspectives in the context of developmental research. Educational Studies in Mathematics, 30, 458–477.CrossRefGoogle Scholar
  7. diSessa, A., & Cobb, P. (2004). Ontological innovation and the role of theory in design experiments. The Journal of the Learning Sciences, 13, 77–104.CrossRefGoogle Scholar
  8. Franke, M. L., Carpenter, T. P., Levi, L., & Fennema, E. (1998, April). Capturing teachers’ generative change: A follow-up study of teachers’ professional development in mathematics. Paper presented at the annual meeting of the American Educational Research Association, San Diego.Google Scholar
  9. Franke, M. L., & Kazemi, E. (2001). Teaching as learning within a community of practice: Characterizing generative growth. In T. Wood, B. Nelson, & J. Warfield (Eds.), Beyond classical pedagogy in elementary mathematics: The nature of facilitative teaching (pp. 47–74). Mahwah, NJ: Lawrence Erlbaum Associates.Google Scholar
  10. Kaput, J. J. (1994). The representational roles of technology in connecting mathematics with authentic experience. In R. Biehler, R. W. Scholz, R. Strasser, & B. Winkelmann (Eds.), Didactics of mathematics as a scientific discipline. Dordrecht: Kluwer.Google Scholar
  11. Lampert, M. (1990). When the problem is not the question and the solution is not the answer: Mathematical knowing and teaching. American Educational Research Journal, 27, 29–63.Google Scholar
  12. Lampert, M. (2001). Teaching problems and the problems in teaching. New Haven, CT: Yale University Press.Google Scholar
  13. Latour, B. (1987). Science in action: How to follow scientists and engineers through society. Cambridge, MA: Harvard University Press.Google Scholar
  14. McClain, K. (2002a). A methodology of classroom teaching experiments. In S. Goodchild & L. English (Eds.), Researching mathematics classrooms: A critical examination of methodology (pp. 91–118). Westport, CT: London, Praeger.Google Scholar
  15. McClain, K. (2002b). Teacher’s and students’ understanding: The role of tools and inscriptions in supporting effective communication. Journal of the Learning Sciences, 11, 217–249.CrossRefGoogle Scholar
  16. McClain, K., & Cobb, P. (1998). The role of imagery and discourse in supporting students’ mathematical development. In M. Lampert & M. Blunk (Eds.), Mathematical talk and school learning: What, why, and how (pp. 56–81). Cambridge: Cambridge University Press.Google Scholar
  17. McClain, K., & Schmitt, P. (2004). Extending teachers’ mathematical understandings: A case from statistical data analysis. Mathematics Teaching in the Middle Schools, 9, 274–279.Google Scholar
  18. McClain, K., Zhao, Q., Visnovska, J., & Bowen, E. (2009). Understanding the role of the institutional context in the relationship between teachers and text. In J. T. Remillard, B. Herbel-Eisenmann & G. Lloyd (Eds.), Mathematics teachers at work: Connecting curriculum materials and classroom instruction. (pp. 56–69). New York: Routledge.Google Scholar
  19. Meira, L. (1995). The microevolution of mathematical representations in children’s activitiy. Cognition and Instruction, 13, 269–313.CrossRefGoogle Scholar
  20. Meira, L. (1998). Making sense of instructional devices: The emergence of transparency in mathematical activity. Journal for Research in Mathematics Education, 29, 121–142.CrossRefGoogle Scholar
  21. Pickering, A. (1995). The Mangle of Practice. Chicago: The University of Chicago Press.Google Scholar
  22. Simon, M. (1995). Reconstructing mathematics pedagogy from a constructivist perspective. Journal for Research in Mathematics Education, 26, 114–145.CrossRefGoogle Scholar
  23. Simon, M. (1997). Developing new models of mathematics teaching. In E. Fennema & B. S. Nelson (Eds.), Mathematics teachers in transition (pp. 55–86). Mahwah, NJ: ErlbaumGoogle Scholar
  24. Steffe, L. P., & Cobb, P. (1988). Construction of arithmetical meanings and strategies. New York: Springer.Google Scholar
  25. Thompson, P. W. (2002). Didactic objects and didactic models in radical constructivism. In K. Gravemeijer, R. Lehrer, B. v. Oers, & L. Verschaffel (Eds.), Symbolizing, modeling and tool use in mathematics education (pp. 197–220). Dordrecht: Kluwer.Google Scholar
  26. van Oers, B. (1996). Learning mathematics as meaningful activity. In P. Nesher, L. Steffe, P. Cobb, G. Goldin, & B. Greer (Eds.), Theories of mathematical learning (pp. 91–114). Hillsdale, NJ: Lawrence Erlbaum Associates.Google Scholar
  27. van Oers, B. (2000). The appropriation of mathematical symbols: A psychosemiotic approach to mathematical learning. In P. Cobb, E. Yackel, & K. McClain (Eds.), Symbolizing and communicating in mathematics classrooms: Perspectives on discourse, tools, and instructional design (pp. 133–176). Mahwah, NJ: Lawrence Erlbaum Associates.Google Scholar
  28. Varela, F. J., Thompson, E., & Rosch, E. (1991) The embodied mind: Cognitive science and human experience. Cambridge, MA: MIT Press.Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Arizona State UniversityPhoenixUSA

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